Torus quantum vortex knots in the Gross-Pitaevskii model for Bose-Einstein condensates

TL;DR

This paper investigates the static and dynamic properties of quantum vortex knots in Bose-Einstein condensates using the Gross-Pitaevskii model, introducing a method to construct and analyze torus knot wave-functions.

Contribution

It presents a new technique to construct the wave-function of torus vortex knots and explores their energy, dynamics, and decay mechanisms within the Bose-Einstein condensate model.

Findings

Torus vortex knots' excitation energy analyzed.

Relationship between topological parameters and velocity established.

Universal decay behavior of non shape-preserving knots confirmed.

Abstract

We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics relating the topological parameter to its translational velocity and characteristic size. We also investigate the breaking mechanisms of non shape-preserving torus knots confirming an evidence of universal decaying behaviour previously observed.